Medical Statistics Made Easy, fourth edition

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Risk ratios (or relative risks) are one way of comparing two proportions. They are calculated with the following equation: MEAN Otherwise known as an arithmetic mean, or average. How important is it? A mean appeared in 2 3 papers surveyed, so it is important to have an understanding of how it is calculated. How easy is it to understand? LLLLL One of the simplest statistical concepts to grasp. However, in most groups that we have taught there has been at least one person who admits not knowing how to calculate the mean, so we do not apologize for including it here. When is it used? It is used when the spread of the data is fairly similar on each side of the mid point, for example when the data are normally distributed. The normal distribution is referred to a lot in statistics. It s the symmetrical, bell-shaped distribution of data shown in Fig. 1. Normal distributions can be entirely defined in terms of the mean and standard deviation in the data set.

In layman’s terms, correlation is how strongly an exposure variable is linked to an outcome variable. A correlation coefficient (r) can be calculated to show how well these two variables are associated and can have a value between -1 and 1. The equation for calculating the correlation coefficient in a parametric data set is below:

range for the variable. For example, if we have some length of hospital stay data with a mean stay of 10 days and a SD of 8 days then: mean – 2 × SD = 10 – 2 × 8 = 10 – 16 = -6 days. This is clearly an impossible value for length of stay, so the data cannot be normally distributed. The mean and SDs are therefore not appropriate measures to use. Good news – it is not necessary to know how to calculate the SD. It is worth learning the figures above off by heart, so a reminder – ±1 SD includes 68.2% of the data ±2 SD includes 95.4%, ±3 SD includes 99.7%. Confidence Intervals 21 However, this will only be the mean for our particular sample. If we took another group of patients we would not expect to get exactly the same value, because chance can also affect the change in BP. The CI gives the range in which the true value (i.e. the mean change in BP if we treated an infinite number of patients) is likely to be. EXAMPLES The average systolic BP before treatment in study A, of a group of 100 hypertensive patients, was 170 mmhg. After treatment with the new drug the mean BP dropped by 20 mmhg. If the 95% CI is 15 25, this means we can be 95% confident that the true effect of treatment is to lower the BP by mmhg. In study B 50 patients were treated with the same drug, also reducing their mean BP by 20 mmhg, but with a wider 95% CI of -5 to +45. This CI includes zero (no change). This means there is more than a 5% chance that there was no true change in BP, and that the drug was actually ineffective. Watch out for... The size of a CI is related to the sample size of the study. Larger studies usually have a narrower CI. Where a few interventions, outcomes or studies are given it is difficult to visualize a long list of means and CIs. Some papers will show a chart to make it easier. For example, meta-analysis is a technique for bringing together results from a number of similar studies to give one overall estimate of effect. Many meta-analyses compare the treatment effects from Chi-squared tests (or Pearson’s chi-squared tests) are applied to establish whether there is a significant difference between two groups of categorical data. It works by comparing the observed data with the data that could be expected if the null hypothesis was true. It is calculated with the following equation: Hypothesis tests allow us to establish the likelihood that the association we are observing is genuine, or simply due to chance. They start with the statement of a null hypothesis – there will not be a significant difference in outcome between the groups. The p-value is effectively the probability that the null hypothesis is true. Therefore, the smaller the p-value becomes, the more likely that the null hypothesis is disproven. When is it used? It is used to represent the average when the data are not symmetrical, for instance the “skewed” distribution in Fig. 2.

This new third edition continues with the same structure as the previous editions and also includes a new section on statistical process controls. A love of statistics is, oddly, not what attracts most young people to a career in medicine and I suspect that many clinicians, like me, have at best a sketchy and incomplete understanding of this difficult subject. Delivering modern, high quality care to patients now relies increasingly on routine reference to scientific papers and journals, rather than traditional textbook learning. Acquiring the skills to appraise medical research papers is a daunting task. Realizing this, Michael Harris and Gordon Taylor have expertly constructed a practical guide for the busy clinician. One a practising NHS doctor, the other a medical statistician with tremendous experience in clinical research, they have produced a unique handbook. It is short, readable and useful, without becoming overly bogged down in the mathematical detail that frankly puts so many of us off the subject. I commend this book to all healthcare professionals, general practitioners and hospital specialists. It covers all the ground necessary to critically evaluate the statistical elements of medical research papers, in a friendly and approachable way. The scoring of each brief chapter in terms of usefulness and ease of comprehension will efficiently guide the busy practitioner through his or her reading. In particular it is almost unique in covering this part of the syllabus for royal college and other postgraduate examinations. Certainly a candidate familiar with the contents of this short book and taking note of its Symbols differ depending on whether they refer to the sample or the real population. Other general symbols and abbreviations are defined below also.

Confounding variables are those which are linked to the outcome but have not been accounted for in the study. For example, we may observe that as ice cream sales increase, so do the number of drownings. This is because ice cream sales will increase in the summer; simultaneously more people will be going for a swim. Therefore there is not a direct causative link between ice creams and drownings, but there is an indirect correlation that we have not accounted for. Fig. 3. Box and whisker plot of energy intake of 50 patients over 24 hours. The ends of the whiskers represent the maximum and minimum values, excluding extreme results like those of the two “nil by mouth” patients. Fig. 7. Graph showing normal distribution of weights of patients enrolling in a trial with mean 80 kg, SD 3 kg. MODE How important is it? Rarely quoted in papers and of limited value. How easy is it to understand? LLLLL An easy concept. When is it used? It is used when we need a label for the most frequently occurring event. What does it mean? The mode is the most common of a set of events. EXAMPLE An eye clinic sister noted the eye-colour of 100 consecutive patients. The results are shown in Fig Number of patients Brown Blue Grey Eye colour Green Fig. 4. Graph of eye colour of patients attending an eye clinic. In this case the mode is brown, the commonest eye colour. Standard deviation, relative risk, confidence intervals, chi-squared and P values Odds ratios and confidence intervals Correlation and regression Survival analysis and risk reduction Sensitivity, specificity and predictive values

Any value on the x-axis of any normal distribution can be converted to a corresponding x-axis value on the standard normal distribution (a z-value) with the following equation: Z value equation Number needed to harm is a similar concept only applied to interventions that have a detrimental effect on patient health. Keeping the “normal distribution” curve in Fig. 6 in mind may help. Examiners may ask what percentages of subjects are included in 1, 2 or 3 SDs from the mean. Again, try to memorize those percentages. From this table, it is clear that if we want a good diagnostic tool, we want a and d to be very much greater than b and c. Sensitivity is defined as the proportion of those with the disease who are correctly identified by the test. In contrast, specificity is the proportion of those without the disease that are correctly identified by the test. Although truly normal distributions are symmetrical about the mean, there may be some distortion in this. One type of distortion is skew. This is where the distribution is not symmetrical and has a more prominent tail pointing in one direction. A tail to the right is described as positive skew, a tail to the left is negative skew (figure 3). This means that the mean, mode and median are no longer equal. Figure 3: Skew 4You may see reference to a “bi-modal distribution”. Generally when this is mentioned in papers it is as a concept rather than from calculating the actual values, e.g. “The data appear to follow a bi-modal distribution”. See Fig. 5 for an example of where there are two “peaks” to the data, i.e. a bi-modal distribution. 400 An understanding of percentages is probably the first and most important concept to understand in statistics! What do they mean? “Per cent” means per hundred, so a percentage describes a proportion of 100. For example 50% is 50 out of 100, or as a fraction 1⁄2. Other common percentages are 25% (25 out of 100 or 1⁄4), 75% (75 out of 100 or 3⁄4). To calculate a percentage, divide the number of items or patients in the category by the total number in the group and multiply by 100. Watch out for... The size of a CI is related to the sample size of the study. Larger studies usually have a narrower CI. Where a few interventions, outcomes or studies are given it is difficult to visualize a long list of means and CIs. Some papers will show a chart to make it easier. For example, “meta-analysis” is a technique for bringing together results from a number of similar studies to give one overall estimate of effect. Many meta-analyses compare the treatment effects from

Using a consistent format, the authors describe the most common statistical methods in turn and then rate them on how difficult they are to understand and how common they are. One of the simplest statistical concepts to grasp. However, in most groups that we have taught there has been at least one person who admits not knowing how to calculate the mean, so we do not apologize for including it here. xii Foreword numerous helpful examination tips should have few difficulties when answering the questions on statistics in both the MCQ and Written modules of the current MRCGP exam. Bill Irish January (BSc MB BChir DCH DRCOG MMEd FRCGP, General Practice Trainer and Examiner for the MRCGP(UK)).

Summary

Not easy, but worth persevering as it is used so frequently. It is not important to know how the P value is derived – just to be able to interpret the result. In a similar fashion to how we could calculate the area under the curve between different points on the x-axis using the SND, we can find the p-value now that we have a z-score. Let’s say our z-score was 1.96. This corresponds to an area under the SND curve of 0.025. This means that beyond 1.96 on the x-axis of the SND lies 2.5% of the data on one side of the curve. Typically, two-sided p-values are used in analyses – this means that the assessment is of the size of the difference to the null hypothesis, not the direction in which that difference is (above or below the mean). It also means we have to double the area we have found as we need to look at points outside of -1.96 as well as 1.96. Based on this we find that 5% of the data lies outside of our interval between -1.96 and 1.96. As 5% is equal to 0.05 as a decimal, our p-value is 0.05 (which by conventional standards is the threshold for statistical significance).